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Discrete Dynamics in Nature and Society
Volume 2013, Article ID 681689, 9 pages
Research Article

Disease Spread in Coupled Populations: Minimizing Response Strategies Costs in Discrete Time Models

1Departamento de Matemáticas, Instituto Tecnológico de Costa Rica, Cartago 30101, Costa Rica
2Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA

Received 6 September 2012; Accepted 19 April 2013

Academic Editor: Francisco Solís Lozano

Copyright © 2013 Geisel Alpízar and Luis F. Gordillo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Social distancing, vaccination, and medical treatments have been extensively studied and widely used to control the spread of infectious diseases. However, it is still a difficult task for health administrators to determine the optimal combination of these strategies when confronting disease outbreaks with limited resources, especially in the case of interconnected populations, where the flow of individuals is usually restricted with the hope of avoiding further contamination. We consider two coupled populations and examine them independently under two variants of well-known discrete time disease models. In both examples we compute approximations for the control levels necessary to minimize costs and quickly contain outbreaks. The main technique used is simulated annealing, a stochastic search optimization tool that, in contrast with traditional analytical methods, allows easy implementation to any number of patches with different kinds of couplings and internal dynamics.